15 citations · 33 across the 14 of their papers we have counts for
16 papers
Stable full-field simulation of a multiscale elliptic equation by means of Quantized Tensor Trains
Marc Josien, Anas El Hachimi, Isabelle Ramière
In this article, we design an original solver based on Quantized Tensor Trains (QTT) for linear elliptic equations with heterogeneous coefficient field, that allows for extremely f…
Regularity theorems for random elliptic operators on domains
Peter Bella, Julian Fischer, Marc Josien +1
Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random ellip…
Dynamic stress response kernels for dislocations and cracks: unified anisotropic Lagrangian formulation
Yves-Patrick Pellegrini, Marc Josien, Martin Chassard
Elastodynamic cohesive-zone models for defects such as cracks or dislocations (such as the Geubelle-Rice model for cracks, or the Dynamic Peierls Equation for flat-core dislocation…
Boundary Layer Estimates in Stochastic Homogenization
Peter Bella, Julian Fischer, Marc Josien +1
We prove quantitative decay estimates for the boundary layer corrector in stochastic homogenization in the case of a half-space boundary. Our estimates are of optimal order and sho…
Shock-driven nucleation and self-organization of dislocations in the dynamical Peierls model
Yves-Patrick Pellegrini, Marc Josien
Dynamic nucleation of dislocations caused by a stress front ('shock') of amplitude moving with speed is investigated by solving numerically the Dynamic Peierls Equa…
Bias in the representative volume element method: periodize the ensemble instead of its realizations
Nicolas Clozeau, Marc Josien, Felix Otto +1
We study the Representative Volume Element (RVE) method, which is a method to approximately infer the effective behavior of a stationary random medium. The latter…
Stochastic homogenization and geometric singularities : a study on corners
Marc Josien, Claudia Raithel, Mathias Schäffner
In this contribution we are interested in the quantitative homogenization properties of linear elliptic equations with homogeneous Dirichlet boundary data in polygonal domains with…
Representative volume elements for matrix-inclusion composites -- a computational study on periodizing the ensemble
Matti Schneider, Marc Josien, Felix Otto
We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper trea…
The annealed Calderon-Zygmund estimate as convenient tool in quantitative stochastic homogenization
Marc Josien, Felix Otto
This article is about the quantitative homogenization theory of linear elliptic equations in divergence form with random coefficients. We derive gradient estimates on the homogeniz…
Quantitative homogenization for the case of an interface between two heterogeneous media
Marc Josien, Claudia Raithel
In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogen…
Precised approximations in elliptic homogenization beyond the periodic setting
Xavier Blanc, Marc Josien, Claude Le Bris
We consider homogenization problems for linear elliptic equations in divergence form. The coecients are assumed to be a local perturbation of some periodic background. We prove $W^…
Decomposition and pointwise estimates of periodic Green functions of some elliptic equations with periodic oscillatory coefficients
Marc Josien
This article is about the -periodic Green function of the multiscale elliptic operator , where …
Mathematical properties of the Weertman equation
Marc Josien
We derive here some mathematical properties of the Weertman equation and show it is the limit of an evolution equation. The Weertman equation is a semilinear integrodifferential eq…
Fourier-based numerical approximation of the Weertman equation for moving dislocations
Marc Josien, Yves-Patrick Pellegrini, Frédéric Legoll +1
This work discusses the numerical approximation of a nonlinear reaction-advection-diffusion equation, which is a dimensionless form of the Weertman equation. This equation models s…
From the Newton equation to the wave equation : the case of shock waves
Xavier Blanc, Marc Josien
We study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, Lions, that this limit is the solution of a nonline…
New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations
Michael Goldman, Marc Josien, Felix Otto
We give a substantially simplified proof of near-optimal estimate on the Kuramoto-Sivashinsky equation from [F. Otto, "Optimal bounds on the Kuramoto-Sivashinsky equation", JFA 200…